scholarly journals Some acyclic systems of permutations are not realizable by triangulations of a product of simplices

2013 ◽  
pp. 317-328
Author(s):  
Francisco Santos
Keyword(s):  
Product Of Simplices

scholarly journals Matching Ensembles (Extended Abstract)

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Suho Oh ◽  
Hwanchul Yoo
Keyword(s):  
Axiom System ◽  
International Audience ◽  
Product Of Simplices

International audience We introduce an axiom system for a collection of matchings that describes the triangulation of product of simplices. Nous introduisons un système d’axiomes pour une collection de couplages qui décrit la triangulation de produit de simplexes.

EQUILIBRIUM IN A DISCRETE EXCHANGE ECONOMY WITH REGIONAL SUB-ECONOMIES

2001 ◽  
Vol 03 (01) ◽  
pp. 57-65
Author(s):  
JUAN C. CESCO ◽  
EZIO MARCHI
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Exchange Economy ◽  
Product Of Simplices

In the first part of this note, we present a generalisation of a lemma due to Gale (1984) to a product of simplices. Then, we use it to derive a permutation-based extension of Browder Fixed Point Theorem proved by Bapat (1989). In the last part, we propose a model of an economy with regional sub-economies in the line of Gale's work (1984) and prove existence equilibrium results under different set of hypothesis.

Product of Simplices and sets of positive upper density in ℝd

2017 ◽  
Vol 165 (1) ◽  
pp. 25-51 ◽  
Author(s):  
NEIL LYALL ◽  
ÁKOS MAGYAR
Keyword(s):  
Direct Proof ◽  
Two Dimensional ◽  
Banach Density ◽  
Upper Density ◽  
Product Of Simplices

AbstractWe establish that any subset of ℝd of positive upper Banach density necessarily contains an isometric copy of all sufficiently large dilates of any fixed two-dimensional rectangle provided d ⩾ 4.We further present an extension of this result to configurations that are the product of two non-degenerate simplices; specifically we show that if Δk1 and Δk2 are two fixed non-degenerate simplices of k1 + 1 and k2 + 1 points respectively, then any subset of ℝd of positive upper Banach density with d ⩾ k1 + k2 + 6 will necessarily contain an isometric copy of all sufficiently large dilates of Δk1 × Δk2.A new direct proof of the fact that any subset of ℝd of positive upper Banach density necessarily contains an isometric copy of all sufficiently large dilates of any fixed non-degenerate simplex of k + 1 points provided d ⩾ k + 1, a result originally due to Bourgain, is also presented.

scholarly journals The number of orientable small covers over a product of simplices

2019 ◽  
Vol 95 (1) ◽  
pp. 1-5
Author(s):  
Murat Altunbulak ◽  
Aslı Güçlükan İlhan
Keyword(s):  
Product Of Simplices

scholarly journals Flow Polytopes of Partitions

10.37236/8114 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Karola Mészáros ◽  
Connor Simpson ◽  
Zoe Wellner
Keyword(s):  
Recent Progress ◽  
Combinatorial Type ◽  
Flow Polytopes ◽  
Work Breaks ◽  
Product Of Simplices ◽  
Product Formulas

Recent progress on flow polytopes indicates many interesting families with product formulas for their volume. These product formulas are all proved using analytic techniques. Our work breaks from this pattern. We define a family of closely related flow polytopes $F_{(\lambda, {\bf a})}$ for each partition shape $\lambda$ and netflow vector ${\bf a}\in Z^n_{> 0}$. In each such family, we prove that there is a polytope (the limiting one in a sense) which is a product of scaled simplices, explaining their product volumes. We also show that the combinatorial type of all polytopes in a fixed family $F_{(\lambda, {\bf a})}$ is the same. When $\lambda$ is a staircase shape and ${\bf a}$ is the all ones vector the latter results specializes to a theorem of the first author with Morales and Rhoades, which shows that the combinatorial type of the Tesler polytope is a product of simplices.

KKM in an arbitrary product of simplices

1996 ◽  
Vol 170 (1) ◽  
pp. 13-21 ◽  
Author(s):  
J. Cesco ◽  
E. Marchi
Keyword(s):  
Product Of Simplices ◽  
Arbitrary Product

scholarly journals Small covers over a product of simplices

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 777-787 ◽  
Author(s):  
Yanchang Chen ◽  
Yanying Wang
Keyword(s):  
Product Of Simplices

In this paper, we determine the number of equivariant homeomorphism classes of small covers over a product of m simplices for m ? 3 or for the dimension of each simplex being greater than 1 and m > 3. Moreover, we calculate the number of equivariant homeomorphism classes of all orientable small covers over a product of at most three simplices.

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